Let Xn be a sequence of p dimensional random vectors. Show that

Xn converges in distribution to $\displaystyle N_p(\mu,\Sigma)$ iff $\displaystyle a'X_n$ converges in distribution to $\displaystyle N_1(a' \mu, a' \Sigma a).$

So I start by finding the MGF to a'Xn:

$\displaystyle E(e^{(a'X_n)t} = E(e^{(a't)X_n}) = e^{a't \mu + 0.5t^2(a' \Sigma a)}$

Hence, {a'Xn} converges $\displaystyle N(a' \mu, a' \Sigma a).$ in distribution.

Is that it, cause I'm not to sure about what I'm supposed to prove.